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4.4 and 4.5: Derivatives of Exponential and Log Functions

4.4 and 4.5: Derivatives of Exponential and Log Functions. Review Properties of Logs and Exponential Function. Inverse: log a x = y a y = x l nx = y e y =x Other properties: ln a x = xlna l oga x = xloga. Properties of Logs and Exponential Functions cont.

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4.4 and 4.5: Derivatives of Exponential and Log Functions

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  1. 4.4 and 4.5: Derivatives of Exponential and Log Functions

  2. Review Properties of Logs and Exponential Function Inverse: logax = y ay = x lnx = y ey=x Other properties: ln ax = xlna logax= xloga

  3. Properties of Logs and Exponential Functions cont. logaax=x lnex = x =x elnx = x Change of base: logax =

  4. Derivative of ex: Derivative of ax:

  5. Examples: Find the derivative. 1. 2. 3. 4.

  6. Find the derivative. 1. 2. 3. 4.

  7. 1. 2.

  8. When does the tangent line to the graph of y = 2t -3 have a slope of 21?

  9. Derivatives of Logarithmic Functions

  10. Find the derivative. 1. 2. 3. 4.

  11. Examples: Find the derivative. 1. 2.

  12. An absolute value inside of a logarithm has no effect on the derivative, other than make the result valid for more x values. (see p. 287) Example: Find the derivative.

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